%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA119^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:45:48 AM UTC 2026
% Result : Theorem 7.04s 3.07s
% Output : Refutation 7.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 19 unt; 0 typ; 2 def)
% Number of atoms : 71 ( 35 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 670 ( 26 ~; 9 |; 1 &; 627 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 41 ( 0 ^; 39 !; 0 ?; 41 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf('type/realax/real_type',type,
'type/realax/real': $tType ).
thf('type/nums/num_type',type,
'type/nums/num': $tType ).
thf('const/realax/real_sub_decl',type,
'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf('const/realax/real_pow_decl',type,
'const/realax/real_pow': 'type/realax/real' > 'type/nums/num' > 'type/realax/real' ).
thf('const/realax/real_of_num_decl',type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf('const/realax/real_neg_decl',type,
'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
thf('const/realax/real_mul_decl',type,
'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf('const/nums/NUMERAL_decl',type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf('const/nums/BIT1_decl',type,
'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
thf('const/nums/_0_decl',type,
'const/nums/_0': 'type/nums/num' ).
thf('const/iterate/sum_decl',type,
'const/iterate/sum':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > 'type/realax/real' ) > 'type/realax/real' ) ).
thf('const/iterate/.._decl',type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf('const/arith/-_decl',type,
'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf('const/arith/<=_decl',type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(sk1_decl,type,
sk1: 'type/realax/real' ).
thf(sk2_decl,type,
sk2: 'type/nums/num' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/realax/real'] :
~ ! [B: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ B )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ A @ B ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ A ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/nums/num'] :
~ ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ A )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sk1 @ A ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ sk1 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ A @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ sk1 ) ) ) ) ) ) ) ).
thf(4,axiom,
! [A: 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ B )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ B ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/REAL_SUB_POW_R1_') ).
thf(14,plain,
! [A: 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ B )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ B ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,plain,
! [B: 'type/nums/num',A: 'type/realax/real'] :
( ~ ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ B )
| ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ B ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ A ) ) ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
! [B: 'type/nums/num',A: 'type/realax/real'] :
( ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ B ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ A ) ) ) )
| ~ ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ B ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(5,axiom,
! [A: 'type/realax/real',B: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_sub' @ A @ B ) )
= ( 'const/realax/real_sub' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realarith/REAL_NEG_SUB_') ).
thf(17,plain,
! [A: 'type/realax/real',B: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_sub' @ A @ B ) )
= ( 'const/realax/real_sub' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_sub' @ A @ B ) )
= ( 'const/realax/real_sub' @ B @ A ) ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_sub' @ A @ B ) )
= ( 'const/realax/real_sub' @ B @ A ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(1,conjecture,
! [A: 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ B )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ A @ B ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/REAL_SUB_POW_L1_') ).
thf(2,negated_conjecture,
~ ! [A: 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ B )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ A @ B ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ B )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ A @ B ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ sk2 )
& ( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sk1 @ sk2 ) )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ sk1 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sk2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ sk1 ) ) ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(9,plain,
( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sk1 @ sk2 ) )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ sk1 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sk2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ sk1 ) ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(10,plain,
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ sk1 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sk2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ sk1 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sk1 @ sk2 ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(39,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ ( 'const/realax/real_sub' @ A @ B ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sk2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ sk1 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sk1 @ sk2 ) ) )
| ( ( 'const/realax/real_sub' @ B @ A )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[19,10]) ).
thf(40,plain,
( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ ( 'const/realax/real_sub' @ sk1 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sk2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ sk1 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( sk1 )),bind(B,$thf( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ))]]) ).
thf(3,axiom,
! [A: 'type/realax/real',B: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ A ) @ B )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/calc_int/REAL_MUL_LNEG_') ).
thf(11,plain,
! [A: 'type/realax/real',B: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ A ) @ B )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ A ) @ B )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ B ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ A ) @ B )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ B ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(43,plain,
( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ sk1 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sk2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ sk1 ) ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sk1 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[40,13]) ).
thf(46,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_sub' @ B @ A )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sk1 @ sk2 ) ) )
| ( ( 'const/realax/real_neg' @ ( 'const/realax/real_sub' @ A @ B ) )
!= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ sk1 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sk2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ sk1 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,43]) ).
thf(53,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( B
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ( A
!= ( 'const/realax/real_pow' @ sk1 @ sk2 ) )
| ( ( 'const/realax/real_sub' @ A @ B )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ sk1 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sk2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ sk1 ) ) ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(59,plain,
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ sk1 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sk2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ sk1 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sk1 @ sk2 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(131,plain,
! [B: 'type/nums/num',A: 'type/realax/real'] :
( ~ ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ B )
| ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ A @ B ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sk1 @ sk2 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ A ) ) )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ sk1 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sk2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ sk1 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,59]) ).
thf(132,plain,
( ~ ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ sk2 )
| ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sk1 @ sk2 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ sk1 @ sk2 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[131:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(151,plain,
~ ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ sk2 ),
inference(simp,[status(thm)],[132]) ).
thf(8,plain,
'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ sk2,
inference(cnfConj,[status(thm)],[7]) ).
thf(165,plain,
~ $true,
inference(rewrite,[status(thm)],[151,8]) ).
thf(166,plain,
$false,
inference(simp,[status(thm)],[165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA119^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n019.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 17:42:32 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.00 % [INFO] Parsing done (206ms).
% 1.22/1.01 % [INFO] Running in sequential loop mode.
% 2.17/1.42 % [INFO] eprover registered as external prover.
% 2.17/1.42 % [INFO] Scanning for conjecture ...
% 2.36/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.36/1.58 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.36/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.55/1.60 % [INFO] Type checking passed.
% 2.55/1.60 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 7.04/3.07 % [INFO] Killing All external provers ...
% 7.04/3.07 % Time passed: 2724ms (effective reasoning time: 2049ms)
% 7.04/3.07 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 7.04/3.07 % Axioms used in derivation (3): thm/iterate/REAL_SUB_POW_R1_, thm/realarith/REAL_NEG_SUB_, thm/calc_int/REAL_MUL_LNEG_
% 7.04/3.07 % No. of inferences in proof: 30
% 7.04/3.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2724 ms resp. 2049 ms w/o parsing
% 7.49/3.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.49/3.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------